Stress analysis of bi-material plane with an elliptic hole by analytical and numerical methods

Abstract

The problems of elasticity for composite materials with holes and inclusions have a great practical significance for mechanics, physics and other areas of science. In this work the analytic solution of a plane problem (plane strain and plane stress) for bi-material plate with an elliptic hole is obtained. A hole is located entirely in a lower half-plane. The constant stresses are given at infinity and on the boundary of the hole an external load is applied. The methods of Kolosov–Muskhelishvili complex potentials, conformal mapping and superposition are used for the solution of the problem. The affinity of a hole to an interface makes essential influence on value of stresses in a vicinity of a hole and on value of stresses at an interface. For engineering applications it is important to know the fields of the stresses and displacements in order to estimate influence of a hole on strength of structure. From considered problems as special cases follow the solutions of problems about a half-plane with an elliptic hole, about an inclined crack in a bi-material plane and half-plane.